1. Lecture 19
A bigger FSM example: Hungry Robot Ant in Maze

2. Robotic ant in a maze Help the ant escape the maze to find food!
Maze has no islands
Food!
start

3. Robotic ant specifics Sensors Actuators What strategy should we use?
L and R antennae, 1 if touching wall
Actuators
F - forward step, TL/TR - turn left/right
What strategy should we use?
Right-hand rule! (It works in physics and pretty much everywhere else…)

4. Right-hand rule
Keep the wall to the right of the ant

5. Special cases: What to do?
Left (L) antenna touching the wall

6. Special cases: What to do?
Ant lost (not adjacent to any wall)

7. Special cases: What to do?
Ant lost (not adjacent to any wall)

8. Robot ant behavior
A: Following wall, touching Go forward, turning left slightly
B: Following wall, not touching Go forward, turning right slightly
D: Hit wall again Back to state A
C: Break in wall Go forward, turning right slightly
E: Wall in front Turn left until...
F: ...we are here, same as state B
G: Turn left until...
LOST: Forward until we touch something

9. Notes and strategy Notes Strategy Maze has no islands
Corridors are wider than ant
Don’t worry about startup
Assume a Moore machine
Assume D flip-flops
Strategy
Right-hand rule!

10. FSM design procedure 1. State diagram 2. State-transition table
3. State minimization
4. State encoding
5. Next-state logic minimization
6. Implement the design

11. Notations Sensors on L and R antennae Movement
Sensor = “1” if touching wall; “0” if not touching wall
L'R'  no wall
L'R  wall on right
LR'  wall on left
LR  wall in front
Movement
F  forward one step
TL  turn left slightly
TR  turn right slightly

12. 1. State diagram Make certain that transitions
L’ R’
L’ R
A/D
[TL, F]
B/C/F
[TR, F]
L’ R
L’ R’
L’ R’
L’ R’ LR
L R’
L R’
G [TL] LR R
E [TL]
L R’ R
L R’
L R’
Make certain that transitions
from all states are defined
on all possible inputs
LOST
(F)
L’ R’ R

13. 2. State transition table
state L R next state outputs
LOST 0 0 LOST F
LOST X 1 E F
LOST 1 0 G F
E 0 0 B TL
E X 1 E TL
E G TL
G 0 0 B TL
G X 1 E TL
G G TL
A 0 0 B TL, F
A 0 1 A TL, F
A 1 0 G TL, F
A E TL, F
B 0 0 B TR, F
B 0 1 A TR, F
B G TR, F
B E TR, F
Same outputs and transitions
 can merge states

14. 3. State minimization Result of merging states E and G L’ R’ L’ R A/D
[TL, F]
B/C/F
[TR, F]
L’ R
L’ R’
L’ R’ L
Result of merging states E and G L
L+R
E/G [TL]
LOST
(F)
L’ R’
L+R

15. 4. State encoding state L R next state outputs X Y X+ Y+ F TR TL
0 0 X X X X
state L R next state outputs
LOST 0 0 LOST F
LOST X 1 E F
LOST 1 0 E F
E 0 0 B TL
E X 1 E TL
E E TL
A 0 0 B TL, F
A 0 1 A TL, F
A 1 X E TL, F
B 0 0 B TR, F
B 0 1 A TR, F
B 1 X E TR, F

16. 5. Next-state logic minimization X X+ Y R L X Y+ Y R L
state L R next state outputs
X Y X+ Y+ F TR TL
0 0 X X X X X F Y R L X TR Y R L X TL Y R L
Why are the 1's in the
last 3 K-maps in vertical
columns?

17. 6. Implement the design
Outputs are a function of the current state only - Moore machine L R F TR TL
Next State
Current State
output logic
next state logic X+ Y+ X Y